A349806 - OEIS

%I #16 Dec 06 2021 11:48:20

%S 14,11,6,5,8,3,2,1,4,11,2,1,8,5,10,3,2,3,4,3,4,1,4,3,4,3,2,1,2,1,4,3,

%T 10,1,2,3,2,13,6,3,4,1,2,1,6,1,6,1,6,1,2,1,2,5,2,3,12,1,6,1,16,1,4,1,

%U 2,3,8,3,2,7,4,7,2,9,2,1,4,1,2,1,22,5,2,5,6,1,2,1,18,5,4,1,2,7,6,1,2,3,8,1,6,1,8,1,4,1,4,1,4,15,12,13,4

%N a(n) = A099610(n) - n^2.

%C a(n) > 0 follows from the definition of A099610.

%H Harvey P. Dale, <a href="/A349806/b349806.txt">Table of n, a(n) for n = 1..1000</a>

%t Module[{nn=120,p2p},p2p=Union[Times@@@Subsets[Prime[Range[2,PrimePi[ Ceiling[ nn^2/3]]]],{2}]];Table[SelectFirst[p2p,#>n^2&]-n^2,{n,nn}]] (* _Harvey P. Dale_, Dec 06 2021 *)

%o (Python)

%o from itertools import count

%o from sympy import factorint

%o def A349806(n):

%o     for i in count(n**2+(n%2)+1,2):

%o         fs = factorint(i)

%o         if len(fs) == 2 == sum(fs.values()):

%o             return i-n**2 # _Chai Wah Wu_, Dec 05 2021

%Y Cf. A099610.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Dec 05 2021